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<H3>create_grid command 
</H3>
<P><B>Syntax:</B>
</P>
<PRE>create_grid Nx Ny Nz keyword args ... 
</PRE>
<UL><LI>Nx,Ny,Nz = size of 1st-level grid in each dimension 

<LI>zero or more keywords/args pairs may be appended 

<LI>keyword = <I>block</I> or <I>clump</I> or <I>random</I> or <I>stride</I> or <I>levels</I> or <I>subset</I> or <I>region</I> or <I>inside</I> 

<PRE>  <I>block</I> args = Px Py Pz
    Px,Py,Pz = # of processors in each dimension, any can be * (see below)
  <I>clump</I> arg = <I>xyz</I> or <I>xzy</I> or <I>yxz</I> or <I>yzx</I> or <I>zxy</I> or <I>zyx</I>
  <I>random</I> args = none
  <I>stride</I> arg = <I>xyz</I> or <I>xzy</I> or <I>yxz</I> or <I>yzx</I> or <I>zxy</I> or <I>zyx</I>
  <I>levels</I> arg = Nlevels
  <I>subset</I> args = Ilevel Px Py Pz Cx Cy Cz
    Ilevel = which level(s) to define, see syntax below
    Px Py Pz = extent of parent cells in each dimension in which to create child cells
    Cx Cy Cz = size of child sub-grid in each dimension within parent cells
  <I>region</I> args = Ilevel reg-ID Cx Cy Cz 
    Ilevel = which level(s) to define, see syntax below
    reg-ID = ID of region which parent cells must be in to create child cells
    Cx Cy Cz = size of child sub-grid in each dimension within parent cells
  <I>inside</I> args = <I>any</I> or <I>all</I> 
</PRE>

</UL>
<P><B>Examples:</B>
</P>
<PRE>create_grid 10 10 10
create_grid 10 10 10 block * * *
create_grid 10 10 10 block 4 2 5
create_grid 10 10 10 levels 4 subset 2*4 * * * 2 2 3
create_grid 20 10 1 levels 2 subset 2 10*15 3*7 1 2 2 1
create_grid 20 10 1 levels 3 region 2 b2 2 2 1 region 3 b3 2 3 1 inside any
create_grid 20 10 1 levels 2 subset 2 10*15 3*7 1 2 2 1 region 3 b3 2 3 1
create_grid 8 8 10 levels 3 subset 2 5* * * 4 4 4 subset 3 1 2*3 3* 2 2 1 
</PRE>
<P><B>Description:</B>
</P>
<P>Overlay a grid over the simulation domain defined by the
<A HREF = "create_box.html">create_box</A> command.  The grid can also be defined by
the <A HREF = "read_grid.html">read_grid</A> command.
</P>
<P>The grid in SPARTA is hierarchical, as described in <A HREF = "Section_howto.html#howto_8">Section howto
4.8</A>.  The entire simulation box is a
single parent grid cell at level 0.  It is subdivided into Nx by Ny by
Nz cells at level 1.  Each of those cells can be a child cell (no
further sub-division) or can be a parent cell which is further
subdivided into Nx by Ny by Nz cells at level 2.  This can recurse to
as many levels as desired.  Different cells can stop recursing at
different levels.  Each level can define its own unique Nx, Ny, Nz
values for subdivision.  Note that a grid with a single level is
simply a uniform grid with Nx by Ny by Nz cells in each dimension.
</P>
<P>Each child grid cell is owned by a unique processor.  The details of
how child cells are assigned to processors by the various options of
this command are described below.  The cells assigned to each
processor will either be "clumped" or "dispersed".
</P>
<P>The <I>block</I> and <I>clump</I> keywords produce clumped assignments of child
cells to each processor.  This means each processor's cells will be
geometrically compact.  The <I>random</I> and <I>stride</I> keywords, produce
dispersed assignments of child cells to each processor.
</P>
<P>IMPORTANT NOTE: See <A HREF = "Section_howto.html#howto_8">Section 6.8</A> of the
manual for an explanation of clumped and dispersed grid cell
assignments and their relative performance trade-offs.  The
<A HREF = "balance_grid.html">balance_grid</A> command can be used after the grid is
created, to assign child cells to processors in different ways.  The
"fix balance" command can be used to re-assign them in a load-balanced
manner periodically during a running simulation.
</P>
<HR>

<P>A single-level grid is defined by specifying only the arguments <I>Nx</I>,
<I>Ny</I>, <I>Nz</I>, with no additional <I>levels</I> keyword.  This will create a
uniform Nx by Ny by Nz grid of child cells.  For 2d simulations, <I>Nz</I>
must equal 1.
</P>
<P>One of the keywords <I>block</I>, <I>clump</I>, <I>random</I>, or <I>strided</I> can be
used to determine which processors are assigned which cells in the
grid.  The <I>inside</I> keyword is ignored for single-level grids.  If no
keyword is used, a setting of block 0 0 0 is the default.
</P>
<P>The <I>block</I> keyword maps the P processors to a <I>Px</I> by <I>Py</I> by <I>Pz</I>
logical grid that overlays the actual <I>Nx</I> by <I>Ny</I> by <I>Nz</I> grid.  This
effectively assigns a contiguous 3d sub-block of cells to each
processor.
</P>
<P>Any of the <I>Px</I>, <I>Py</I>, <I>Pz</I> parameters can be specified with an
asterisk "*", in which case SPARTA will choose the number of
processors in that dimension.  It will do this based on the size and
shape of the global grid so as to minimize the surface-to-volume ratio
of each processor's sub-block of cells.
</P>
<P>The product of Px, Py, Pz must equal P, the total # of processors
SPARTA is running on.  For a 2d simulation, Pz must equal 1. If
multiple partitions are being used then P is the number of processors
in this partition; see <A HREF = "Section_start.html#start_6">Section 2.6</A> for an
explanation of the -partition command-line switch.
</P>
<P>Note that if you run on a large, prime number of processors P, then a
grid such as 1 x P x 1 will be required, which may incur extra
communication costs.
</P>
<P>The <I>random</I> keyword means that each grid cell will be assigned
randomly to one of the processors.  Note that in this case different
processors will typically not be assigned exactly the same number of
cells.
</P>
<P>The <I>clump</I> keyword means that the Pth clump of cells is assigned to
the same processor, where P is the number of processors.  E.g. if
there are N = 100 cells and 10 processors, then the 1st processor
(proc 0) will be assigned cells 1 to 10.  The 2nd processor (proc 1)
will be assigned cells 11 to 20.  And The 10th processor (proc 9) will
be assigned cells 91 to 100.
</P>
<P>The <I>stride</I> keyword means that every Pth cell is assigned to the same
processor, where P is the number of processors.  E.g. if there are 100
cells and 10 processors, then the 1st processor (proc 0) will be
assigned cells 1,11,21, ..., 91.  The 2nd processor (proc 1) will be
assigned cells 2,12,22 ..., 92.  The 10th processor (proc 9) will be
assigned cells 10,20,30, ..., 100.
</P>
<P>The argument for <I>stride</I> and <I>clump</I> determines how the N grid cells
are ordered and is some permutation of the letters <I>x</I>, <I>y</I>, and <I>z</I>.
Each of the N cells has 3 indices (I,J,K) to describe its location in
the 3d grid.  If the stride argument is yxz, then the cells will be
ordered from 1 to N with the y dimension (J index) varying fastest,
the x dimension next (I index), and the z dimension slowest (K index).
</P>
<HR>

<P>A hierarchical grid with more than one level can be defined using the
<I>levels</I> keyword.  The <I>Nlevels</I> argument is the number of levels
which must be 2 or more.  The entire simulation box is level 0 in the
hierarchy.  The settings for Nx,Ny,Nz specify the level 1 grid.  All
other levels must be defined by using either the <I>subset</I> or <I>region</I>
keyword in addition to the <I>levels</I> keyword.
</P>
<P>A <I>block</I>, <I>clump</I>, <I>random</I>, or <I>stride</I> keyword can be specified in
addition to the <I>levels</I> keyword for a hierarchical grid.  As
described above, they determine how level 1 grid cells are assigned to
processors, as described above.  In the hierarchical case all grid
cells of level 2 or higher that are within a single level 1 cells are
assigned to the processor that owns the level 1 cell.
</P>
<P>The settings for every level, from 2 to Nlevels, must be specified
exactly once via the <I>Ilevel</I> argument to either a <I>subset</I> or
<I>region</I> keyword.  <I>Ilevel</I> can be specfied as a single number or use
a wildcard asterisk in place of or in conjuction with one or two
integers to specify multiple levels at the same time.  This takes the
form “*” or “*n” or “n*” or “m*n”.  An asterisk with no numeric values
means all levels from 2 to Nlevels.  A leading asterisk means all
levels from 2 to n (inclusive). A trailing asterisk means all levels
from n to Nlevels (inclusive). A middle asterisk means all levels from
m to n (inclusive).
</P>
<P>For the <I>subset</I> keyword, the Px, Py, Pz arguments specify which cells
in the previous level are flagged as parents and sub-divided to create
cells at the new level.  For example, if the level 1 grid is
100x100x100, then Px, Py, Pz for level 2 could select any contiguous
range of cells from 1 to 100 in x, y, or z.  If the level 2 grid is
4x4x2 within any level 1 cell (as set by Cx, Cy, Cz), then Px, Py, Pz
for level 3 could select any contiguous range of cells from 1 to 4 in
x, y and 1 to 2 in z.  Each of the Px, Py, Pz arguments can be a
single number or be specified with a wildcard asterisk, the same as
described above for <I>Ilevel</I>, where the bounds of Px (for example) are
1 to Cx in the preceeding parent level.
</P>
<P>The Cx, Cy, Cz arguments are the number of new cells (in each
dimension) to partition each selected parent cell into.  <I>Cz</I> must be
one for 2d.  Any of Cx, Cy, Cz may have a value of 1, but they cannot
all be 1.  Note that for each new level, only grid cells that exist in
the previous level are partitioned further.  E.g. level 3 cells are
only added to level 2 cells that exist, since some level 1 cells may
not have been partitioned into level 2 cells.
</P>
<P>For example this command creates a two-level grid:
</P>
<PRE>create_grid 10 10 10 levels 2 subset 2 * * * 2 2 3 
</PRE>
<P>The 1st level is 10x10x10.  Each of the 1000 level 1 cells is further
partitioned into 2x2x3 cells.  This means the total number of
resulting grid cells is 1000 * 12 = 12000.
</P>
<P>This command creates a 3-level grid:
</P>
<PRE>create_grid 8 8 10 levels 3 subset 2 5* * * 4 4 4 subset 3 1 2*3 3* 2 2 1 
</PRE>
<P>The first level is 8x8x10.  The second level is 4x4x4 within each
level 1 cell, but only half or 320 of the 640 level 1 cells are
sub-divided, namely those with x indices from 5 to 8.  Those with x
indices from 1 to 4 remain as level 1 cells.  Some of the level 2
cells are further partitioned into 2x2x1 level 3 cells.  For the 4x4x4
level 2 grid within 320 or the level 1 cells, only the level 2 cells
with x index = 1, y index = 2-3, and z-index = 3-4 are further
partitioned into level 3 cells, which is just 4 of the 64 level 2
cells.  The resulting grid thus has 24640 grid cells: 320 level 1
cells, 19200 level 2 cells, and 5120 level 3 cells.
</P>
<P>For the <I>region</I> keyword, the subset of cells in the previous level
which are flagged as parents and sub-divided is determined by which of
them are in the geometric region specified by <I>reg-ID</I>.
</P>
<P>The <A HREF = "region.html">region</A> command can define volumes for simple
geometric objects such as a sphere or rectangular block.  It can also
define unions or intersections of simple objects or other union or
intersection objects.  by defining an appropriate region, a complex
portion of the simulation domain can be refined to a new level.
</P>
<P>Each grid cell at the previous level is tested to see whether it is
"in" the region.  The <I>inside</I> keyword determines how this is done.
If <I>inside</I> is set to <I>any</I>, which is the default, then a grid cell is
in the region if any of its corner points (4 in 2d, 8 in 3d) is in the
region.  If <I>inside</I> is set to <I>all</I>, then all 4 or 8 of its corner
points must be in the region for a grid cell to be in the region.
Note that the <I>side</I> option for the <A HREF = "region.html">region</A> command can
be used to define whether the inside or outside of the geometric
region is considered to be "in" the region.
</P>
<P>If the grid cell is in the region, then it is refined using the Cx,
Cy, Cz arguments in the same way the <I>subset</I> keyword uses them.
Examples using the <I>region</I> keyword are given above.
</P>
<HR>

<P><B>Restrictions:</B>
</P>
<P>This command can only be used after the simulation box is defined by
the <A HREF = "create_box.html">create_box</A> command.
</P>
<P><B>Related commands:</B>
</P>
<P><A HREF = "create_box.html">create_box</A>, <A HREF = "read_grid.html">read_grid</A>
</P>
<P><B>Default:</B>
</P>
<P>The default setting for block vs clump vs random vs stride is block
with Px = Py = Pz = *.  The inside keyword has a default setting of
any.
</P>
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